WASHINGTON (Reuters) - Teresa Heinz Kerry's condition was upgraded to fair from critical on Monday, a day after the wife of U.S. Secretary of State John Kerry was rushed to the hospital with an unspecified illness, the State Department said on Monday.

Earlier on Monday, a source said her family believed Heinz Kerry, 74, might have suffered a seizure before she was taken to a hospital on the Massachusetts island of Nantucket and then flown in her own plane to be treated at Boston's Massachusetts General Hospital.

"After conducting tests overnight and this morning, doctors at Massachusetts General Hospital have upgraded Mrs. Teresa Heinz Kerry's condition from critical to fair," Kerry spokesman Glen Johnson said in a written statement.

"She is undergoing further evaluation, and Secretary of State John Kerry, her son, and other family members remain with Mrs. Heinz Kerry at the hospital in Boston, as they have been since she became ill," Johnson said.

Speaking on condition of anonymity, a source close to the family had earlier said family members "saw her exhibiting symptoms consistent with a seizure" on Sunday but stressed that her condition was still being assessed by doctors.

Heinz Kerry, a philanthropist and heiress, was born in the southern African nation of Mozambique and was married to Republican Pennsylvania Senator John Heinz III, an heir to the Heinz food fortune, until his death in a 1991 helicopter crash.

In 1995, she married Kerry, who at the time was a Democratic U.S. senator from Massachusetts, on Nantucket.

Kerry's second wife, she is the chairman of the Heinz Endowments and the Heinz Family Philanthropies. She is active in environmental issues, has served on numerous boards and has been awarded 10 honorary degrees, according to the Heinz Endowment.

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